EP1166435A1

EP1166435A1 - Non-linear distortion generator

Info

Publication number: EP1166435A1
Application number: EP00919766A
Authority: EP
Inventors: Shutong Zhou; Timothy J. Brophy; Richard A. Meier
Original assignee: Arris Technology Inc; General Instrument Corp
Current assignee: Arris Technology Inc
Priority date: 1999-04-01
Filing date: 2000-03-29
Publication date: 2002-01-02
Anticipated expiration: 2020-03-29
Also published as: WO2000060734A1; DE60005163D1; KR20010111287A; US20010054927A1; EP1166435B1; MXPA01009899A; US6577177B2; TW498603B; AU4039700A; ES2206218T3; ATE249693T1; DE60005163T2; AU761636B2; CA2368578A1; CN1345478A

Abstract

An in-line distortion generator for coupling in-line with a non-linear device (NLD) produces an output signal of useful amplitude, but with low composite triple beat and cross modulation distortions. The distortion generator comprises an instant controlled non-linear attenuator which utilizes the non-linear current flowing through a pair of diodes to provide the proper amount of signal attenuation over the entire frequency bandwidth. The distortion generator circuitry is always matched to the NLD, thereby ensuring a frequency response that is predictable and predefined. The distortion generator may also include a temperature compensation circuit to ensure consistent operation throughout a wide temperature range.

Description

NON-LINEAR DISTORTION GENERATOR

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates generally to communication systems employing

amplification devices. More particularly, the invention pertains to a non-linear

predistortion or postdistortion generator for coupling in-line with an amplifier,

optical detector or laser to minimize the signal distortion caused by amplification.

Description of the Related Art

Amplifiers are widely used in many types of communication applications.

Although it is preferable to keep amplifiers within their linear range of operation, it

has been increasingly necessary to extend the operation of amplifiers into high power

and high frequency regions of operation. Typically, the output power of an amplifier

is limited by the non-linearity of the active devices, including bipolar transistors and

FETs. These non-linearities result in distortions which are impressed upon the signal

being amplified. Reducing the non-linear distortions of an amplifier results in

increases of the output power, the system dynamic range and the carrier-to-noise

ratio. Accordingly, minimizing distortions and achieving linear frequency response

is paramount to efficient amplifier operation.

Minimizing distortion is particularly important when a series of amplifiers is

cascaded over a signal transmission path, such as a series of RF amplifiers in a

CATV transmission system. Disposed throughout a CATV transmission system are

RF amplifiers that periodically amplify the transmitted signals to counteract cable attenuation and attenuation caused by passive CATV components, such as, signal

splitters and equalizers. The RF amplifiers are also employed to maintain the desired

carrier-to-noise ratio. Due to the number of RF amplifiers employed in a given

CATV transmission system, each RF amplifier must provide minimum degradation

to the transmitted signal.

Many amplifiers are subject to a wide range of ambient operating

temperatures. These temperature changes may affect the operating characteristics of

certain electronic components within the amplifier, thereby inducing additional

distortions. A temperature range of -40°C to +85 °C is not uncommon for many

amplifier applications in a communication environment. To ensure consistent

performance over the operating bandwidth, and to minimize resulting distortions, an

amplifier must be designed for a broad range of ambient operating temperatures.

The distortions created by an amplifier which are of primary concern are

second (even) and third (odd) order harmonic intermodulation and distortions. Prior

art amplifier designs have attempted to ameliorate the effects of even order

distortions by employing push-pull amplifier topologies, since the maximum second

order cancellation occurs when equal amplitude and 180° phase relationship is

maintained over the entire bandwidth. This is achieved through equal gain in both

push-pull halves by matching the operating characteristics of the active devices.

However, odd-order distortion is difficult to remedy. Odd-order distortion

characteristics of an amplifier are manifest as cross modulation (X-mod) and

composite triple beat (CTB) distortions on the signal being amplified. X-mod occurs when the modulated contents of one channel being transmitted interferes with and

becomes part of an adjacent or non-adjacent channel. CTB results from the

combination of three frequencies of carriers occurring in the proximity of each

carrier since the carriers are typically equally spaced across the frequency bandwidth.

Of the two noted distortions, CTB becomes more problematic when increasing the

number of channels on a given CATV system. While X-mod distortion also

increases in proportion to the number of channels, the possibility of CTB is more

dramatic due to the increased number of available combinations from among the

total number of transmitted channels. As the number of channels transmitted by a

communication system increases, or the channels reside close together, the odd-order

distortion becomes a limiting factor of amplifier performance.

There are three basic ways of correcting distortion created by a non-linear

device (NLD): 1) reduce the signal power level; 2) use a feed forward technique;

and 3) use a predistortion or postdistortion technique. The first method reduces the

signal power level such that the NLD is operating in its linear region. However, in

the case of an RF amplifier this results in very high power consumption for low RF

output power.

The second method is the feed forward technique. Using this technique, the

input signal of the main amplification circuit is sampled and compared to the output

signal to determine the difference between the signals. From this difference, the

distortion component is extracted. This distortion component is then amplified by

an auxiliary amplification circuit and combined with the output of the main amplification circuit such that the two distortion components cancel each other.

Although this improves the distortion characteristics of the amplifier, the power

consumed by the auxiliary amplification circuit is comparable to that consumed by

the main amplification circuit. This circuitry is also complex and very temperature

sensitive.

The third method is the predistortion or postdistortion technique. Depending

upon whether the compensating distortion signal is generated before the non-linear

device or after, the respective term predistortion or postdistortion is used. In this

technique, a distortion signal equal in amplitude but opposite in phase to the

distortion component generated by the amplifier circuit is estimated and generated.

This is used to cancel the distortion at the input (for predistortion) or output (for

postdistortion) of the amplifier, thereby improving the operating characteristics of

the amplifier.

One such distortion design, as disclosed in U.S. Patent No. 5,703,530 and

shown in Figure 1, relies upon a traditional π-attenuation network and a delay line

for gain compensation; and a diode pair coupled with a delay line for distortion and

phase compensation. This circuit generates a distortion that is equal in amplitude but

opposite in phase to the distortion introduced by the amplifier. Plots of the

distortions contributed by the distortion generator and the distortions manifest by the

amplifier are shown in Figures 2 and 3. As shown, the distortion signal compensates

for the distortions generated by the amplifier. However, the use of delay lines in

such a manner is impractical since delay lines are physically large, are difficult to adjust and the results are inconsistent across a wide frequency range. Additionally,

both amplitude and phase information are required for correct compensation. The

'530 patent also states that the system disclosed therein is not ideal for certain

application, such as predistortion for CATV RF amplifiers, due to the excessive

losses introduced by the distortion circuit.

An inline predistortion design, as disclosed in U.S. Patent No. 5,798,854,

provides compensation for NLDs by applying a predistorted signal equal in

magnitude but opposite in phase to the distortion produced by the NLD. However,

the circuitry disclosed therein is not matched to the NLD. Additionally, the '854

patent presents a design that is typical of the prior art in the use of a high resistance

bias for the diodes. This will reduce the correction efficiency and increase the

effects of temperature upon the circuit.

Accordingly, there exists a need for a simple distortion generator which

counteracts the distortion created by an NLD. The circuit should not introduce

additional signal delay and should operate over a wide frequency bandwidth and

wide ambient temperature range.

SUMMARY OF THE INVENTION

The present invention is an in-line predistortion or postdistortion generator

for coupling in-line with an NLD to produce an output signal of useful amplitude,

but with low composite triple beat and cross modulation distortions. The distortion

generator comprises an instant controlled non-linear attenuator which utilizes the non-linear current flowing through a pair of diodes to provide the proper amount of

signal attenuation over the entire frequency bandwidth. The distortion generator

circuitry is always matched to the NLD, thereby ensuring a frequency response that

is predictable and predefined. The distortion generator also includes a temperature

compensation circuit to ensure consistent operation throughout a wide temperature

range.

Accordingly, it is an object of the present invention to provide a temperature

compensated distortion generator which minimizes cross modulation and composite

triple beat distortions manifested by an NLD such as an RF amplifier, a laser diode

or a photodetector.

Other objects and advantages of the of the present invention will become

apparent to those skilled in the art after reading a detailed description of the preferred

embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of a prior art distortion generator.

Figure 2 is a combination plot of the effect of using the outputs from the prior

art distortion generator shown in Figure 1 with an RF amplifier.

Figure 3 is a combination plot of the effect of using the outputs from the prior

art distortion generator shown in Figure 1 with an RF amplifier.

Figure 4 is schematic diagram of a π attenuator. Figure 5 is a signal diagram of the diode non-linear current caused by the

input voltage.

Figure 6 is a schematic diagram of the preferred embodiment of the distortion

generator of the present invention.

Figure 7 is a schematic diagram of the temperature compensation circuit.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiment of the present invention will be described with

reference to the drawing figures where like numerals represent like elements

throughout. Although the preferred embodiment of the present invention will be

described, for simplicity of explanation, as being coupled with an RF amplifier, those

skilled in the art would clearly recognize that such a distortion generator could also

be utilized to compensate for distortion in laser transmitters, optical detectors, and

other electronic components which operate over a wide range of frequencies. The

description herein is not intended to be limiting, rather it is intended to be

illustrative.

The present invention will be described with reference to Figure 4, whereby

a π attenuator network 20 is shown. The network 20 comprises a selected

configuration of resistors Zj, R_x, R₂, R₃, Z₀, R_p. The signal source is input at signal

input 30 and the output of the attenuator network 20 is seen across the output 95.

Z_j is the source of internal impedance which should be equal to the system

impedance Z₀, which is seen across the output 95. In an embodiment of the invention for use with a CATV system, the impedance values Z, and Z₀ are equal to

75 Ohms. Three of the resistors R_x, R₂, R₃ form a π attenuator configuration.

Preferably, the values (Y) of resistors R₂ and R₃ are equal, and substantially larger

than the value (X) of resistor R, . Resistor R_p is connected in parallel with resistor

As one skilled in the art would clearly recognize, when the following

condition is satisfied:

X = 2Z₀ ² Y/ (Y² - Z₀ ²) Equation (1)

the attenuator network 20 is matched at input and output, from D.C. to very high

frequencies. For one example of the attenuator when X = 7.5 and Y = 1.5K, the

power attenuation A for this attenuator network 20 is:

2 (YZo / (Y + Zo) + X )Y (YZo / (Y + Zo)) Equation (2)

(Y + X + Y Zo / (Y + Zo)) (X + (YZo / (Y + Zo)))

A = ( )²

(YZo / (Y + Zo) + X )Y

Y + X + YZo / (Y + Zo)

Under the condition when Z₀ « Y, (as is the case when X = 7.5 and Y = 1.5K):

A * (2 Z₀ / (2 Z₀ + X))² Equation (3)

A (dB) = 10 lg A Equation (4)

When X = 7.5 and Y = 1.5k, A (dB) = 0.42dB. This means the attenuator network

20 has very low insertion losses and a good frequency response. When X has a small

variation due to the parallel of R , shown in Figure 4, from Equation (3) Delta X

D elta A (dB ) = - 8.68 Equation (5) 2Zo + X

XR, X_

Delta X = X = Equation (6)

X + R_P R_P

From Equation (6):

X

D elta A (dB ) ≡ 8.68 Equation (7)

2Zo R_t

For example, If R = 375 ohms then:

7.5 7.5 D elta A (dB ) = 8.68 ^•———— = 0.00868dB Equation (8)

Equation (8) shows that when R_p (375 ohms) is in parallel with W_x (7.5 ohms), the

attenuation will be reduced by 0.00868dB. This amount of attenuation change is

needed for non-linear compensation for an amplifier. This example also shows that

when the value of R_p » R,, (i.e., when R_p is 50 times larger than R,), adding R_p

parallel with R, has almost no effect on the impedance match, and the voltage drop

over the R_p is mainly determined by the value of R,.

However, if a linear resistor R_p is used in the attenuator network 20, there will

be no distortion signal produced. The attenuator network 20 as shown is a linear

device. In order for a distortion circuit to operate effectively, diodes are used to

create a non-linear resistance. Preferably, Schottky diodes are utilized. At small current, diode current is exponentially proportional to the voltage across over the

diode. Thus diodes can be used as a non-linear resistance. For non-linear

applications, the amount of attenuation can be calculated as:

D elta A (dB ) = 8.68 Equation (9)

Where I_p is the current flow through R_p, (the non-linear resistance). I_j is the

current flow through R, . Equation 9 provides the relationship of the attenuation

change due to the current change in I_p. This equation is accurate over a broad

frequency range. The relationship between the delta attenuation and a change in

current is still valid when the resistance is a non-linear resistor. Accordingly,

Equation 9 provides a good estimation of how much non- linear current is required

for predistortion or postdistortion purposes.

Referring to Figure 5, when the input sinusoidal voltage wave changes from

V, to V₂ to V₃, the output current changes from I, to I₂ to I₃ respectively. The non¬

linear current used for third order correction is:

I nonlinear = Ii - 2 h + h Equation (10)

From Equation 9, the non-linear current needed is:

X 1 nonlinear

D elta A nonlinear correction (dB ) ≡ 8 .68 - Equation (11)

2Zθ I output

Only non-linear current will be useful for predistortion or postdistortion

purposes. Equation 11 can be rewritten in the form of : Inon near eff D elta A nonlinear correction (dB ) = 8.68 Equation (12) loutput

Inonhnear

In onlmear eff Equation (13)

Accordingly, I_non._{lιnear eff} in Equation 12 is the effective non-linear current

going to the output port 114 which is shown in Figure 6. I_output in Equation 12 is the

total current that goes to the output port 114. Equation 13 shows that only a small

part of the non-linear diode current is effectively being used for correction.

The π attenuator network 20 has low insertion loss and the voltage drop of

the input voltage on R_x (shown in Figure 4) is proportional to the input voltage.

This voltage may be used to drive a pair of diodes to produce non-linear current.

The non-linear current flowing in the diodes will cause an attenuator to provide less

attenuation at larger RF amplitudes, (i.e. when the input signal has a higher power).

This may be used to compensate for the signal compression caused by amplification.

Because of the relatively high value of the diode's non-linear resistance, the match

of the attenuator network is almost unchanged. This match will not be changed even

over temperature. Additionally, frequency response over multi-octave frequency

bands is favorable.

Referring to Figure 6, the preferred embodiment of the attenuator 100 for

predistortion and postdistortion is shown. The attenuator 100 of the present

invention includes several additional components that modify a traditional π attenuator to achieve significantly better performance over a wide frequency and

temperature range. The attenuator 100 has an input port 101, an output port 114 and

a bias control port 116. The attenuator 100 may be used in a predistortion

configuration with an amplifier or in a postdistortion configuration. For a

predistortion configuration, the output port 114 is connected to the input of an

amplifier. For the postdistortion configuration as shown in Figure 6, an output

signal generated by an amplifier, is applied to the input port 101. The attenuator 100

includes resistors 105, 106, 107, 108, 112; capacitors 102, 103, 104, 111, 113, 115;

diodes 109, 110, and an inductor 117.

The inductor 117 is used in series with the resistor 108. The function of the

inductor 117 is to make a parallel resonance circuit with the forward biased diode

capacitor. At the resonance frequency, the capacitance of the diode will be

compensated by the inductor 117 so that the impedance between points 118 and 119

will be pure resistive and can be calculated as follows:

R impedance between 118, 119 = L / (C * R ) ; Equation (14)

where L is the inductance of 117 in Henrys; C is the total forward biased capacitor

in Farads; and R is the resistance 108 in Ohms. By carefully controlling L and C,

one may get the following:

R impedance between 118. 119 = R E UaUOn (15)

This means the capacitive effect has been totally canceled and an ideal pure resistive

load over a very wide frequency range has been achieved. The function of the resistors 105, 106, 107, 108, 112 and the capacitors 102,

103, 104, 111, 113, 115 is to form a modified π attenuation network in comparison

to the π attenuation network 20 shown in Figure 4. The capacitors 102, 103, 104,

111, 113, and 115 are also used for D.C. blocking and AC coupling. From an AC

standpoint, the parallel combination of resistors 105 and 106 is functionally

equivalent to resistor R₂ of Figure 4. Preferably, the values of resistors 105 and 106

should be chosen such that the parallel combination is equivalent to the value of

resistance of resistor 112, (i.e. ((R^R_IOOVC _IOS+R_IOO)) = R-m)- Resistor 108 is

functionally equivalent to resistor R_α of Figure 4; and the in-series combination of

resistor 112 and capacitor 111 is functionally equivalent to resistor R₃ of Figure 4.

The value of resistor 107 has no effect on RF signal attenuation.

The other function for resistors 105, 106, and 107 is to supply a D.C. bias to

the diodes 109, 110. The diodes 109, 110 are first connected in series; and the series

combination is connected to resistor 107 in parallel. Because resistor 107 has a low

resistance value and is in parallel with the diodes 109, 110, the voltage drop across

the diodes 109, 110 will be primarily determined by the resistance of resistor 107.

If the D.C. current flow in resistor 107 is much more than the current flow in the

diodes 109, 110, D.C. the voltage drop across the diode 109, 110, will be very stable

and will be insensitive to the presence or absence of a signal at the input port 101.

The integrated functions of signal attenuation and diode bias supply avoid any

parasitic effects due to the introduction of additional bias circuitry. This permits a

high frequency response and a favorable impedance match. From a D.C. perspective, resistor 107, in parallel with capacitors 103 and 104,

provides a dissipative circuit to the capacitors 103, 104. Therefore, resistor 107 will

discharge the accumulated electric charge of connected capacitors 103, 104 in every

AC cycle.

Diode 109 is connected to resistor 108 through capacitor 104 while diode 110

is connected to resistor 108 through capacitor 103. Diode 109 is responsible for the

RF distortion correction during the negative portion of the AC cycle, while the diode

110 has the same function during the positive half of the AC cycle. The non-linear

current of diode 109 charges capacitor 104, and the non-linear current of diode 110

charges capacitor 103. Due to the configuration of the circuit, the voltage produced

on capacitors 103 and 104 have the same value but different signs. The small

resistance from resistor 107 connected to the capacitors 103, 104 discharges the

accumulated electric charge during every AC cycle. As a result, there is no

additional D.C. voltage drop across the capacitors 103, 104 due to the input RF

signals. This permits the diode 109, 110 to provide the largest non-linear current for

the correction purpose.

The present invention has several unique advantages over the prior art. Due

to its symmetric structure, the attenuator 100 produces only odd order distortion.

Consequently, the circuit does not degrade the second order performance of an NLD.

The attenuator 100 also uses two low series resistances 107, 108. From a D.C.

perspective, resistor 107 significantly improves the correction efficiency and reduces

the susceptibility to ambient temperature effects. From an AC perspective, resistor 108 provides for distortion correction with low insertion losses. Due to the

attenuator 100 design, the voltage drop across resistor 108 fully loads the diodes 109,

110 even under non-linear operation of the diodes 109, 110. As a result, maximum

non-linear current is utilized for correction purposes. Finally, proper phasing of the

distortion signals is inherent in the design, thereby avoiding additional phase

circuitry and delay lines. This permits a circuit design which is much less complex

and results in a compact and robust design.

The present attenuator design uses low series resistance 108. The inductor

117 in series with the resistance 108 compensates for the capacitance of the diodes.

Thus, the third order correction circuit may work over a wide frequency range and

wide temperature range. This correction circuit design is flexible and may be

adjusted to different kinds of RF hybrids with different distortion characteristics.

This circuit is always matched to its input side and output side over wide frequency

range.

Table 1 provides a listing of the components shown in Figure 6. However,

one skilled in the art would clearly recognize that the values shown in Table 1 are

only for explanatory purposes, and should not be considered to be limiting to the

invention. For example, the value of resistor 108 may range from approximately 2Ω

to 30Ω. Likewise, the value of resistor 107 may range from approximately 100Ω to

3000Ω. TABLE 1

As previously described, the attenuator 100 uses the non-linear current

produced by the diodes 109, 110 to compensate for the voltage compression caused

by an NLD. As shown, the attenuator 100 comprises capacitance, resistance and two

diodes. The diodes are the only components that are sensitive to temperature change

and the only components that require correction during operation over a wide

temperature range. There are three factors which must be taken into consideration

when operating the attenuator 100 over a wide temperature range: 1) The diode operating current will change if the bias voltage remains

constant while the ambient temperature changes. Under the same input voltage swing

at the input port 101 and the same bias voltage, more non-linear diode current will

be created as the ambient temperature rises.

2) When the ambient temperature rises, the diode will produce less non¬

linear correction current for the same input signal voltage and the same diode bias

current.

3) NLDs typically exhibit more distortion as the ambient temperature rises.

Accordingly, a higher diode non-linear current is required for correction of the

greater distortion.

All of the temperature effects experienced by the attenuator 100 are related to

the bias voltage. Some of the effects are additive while others are subtractive.

However, the result is that for a given temperature, there will be an optimum bias

voltage to produce the proper correction output. Proper temperature correction will

be achieved when there is a predefined change of bias voltage verses temperature.

Referring to Figure 7, the preferred embodiment of the temperature

compensation circuit 200 is shown. The temperature compensation circuit 200

controls the bias of the diodes 109, 110 (shown in Figure 6) for optimum

compensation of the distortion. As shown, the temperature compensation circuit 200

comprises two transistors 206, 213; a capacitor 216; nine resistors 201, 202, 203, 204,

207, 209, 210, 214, 215; two diodes 205, 208; and a negative temperature coefficient

thermistor 211. The negative temperature coefficient thermistor 211 is coupled in parallel with

resistor 210 to form a temperature linearized resistance, which is correlated to a

change in temperature. The PNP transistor 206 provides a constant current source

through its collector to the linearized resistor combination 210, 211. The constant

current provided by the PNP transistor 206 induces a linearized voltage change across

the resistor combination 210, 211 as the temperature changes. By adjusting the value

of the variable resistor 202, the amount of constant current through the PNP transistor

206 can be changed. Therefore, the voltage swing over temperature can be changed.

The constant current also passes through the variable resistor 209, thereby creating

a constant voltage drop that is used as a starting bias point for bias voltage

adjustment. By selectively adjusting the resistance of resistors 202 and 209, any

combination of voltage swing and starting bias voltage can be obtained. A NPN

transistor 213, which is an emitter follower transistor, provides the control bias

voltage from line 217 through line 116 to the attenuator 100, as shown in Figure 7.

The two diodes 205 and 208 are used to compensate for the junction voltage of the

two transistors 206, 213 which change over temperature.

Table 2 provides a listing of the components shown in Figure 7. However,

one skilled in the art would clearly recognize that the values shown in Table 2 are

only for example, and should not be considered to be limiting to the invention. TABLE 2

It should be recognized that the present invention provides an instant voltage

controlled non-linear attenuator design combined with a bias supply for optimum

non-linear correction efficiency and bias temperature stability. Even if the

temperature compensation circuit 200 as disclosed herein is not utilized, the preferred

embodiment of the present invention provides adequate distortion correction over a

broad temperature range. When the temperature compensation circuit 200 is utilized, the distortion compensation results can be further improved. Accordingly, a trade off

between the performance of the compensating circuit and the complexity of the

circuit must be weighted.

Claims

What is claimed is:

1. An external distortion control circuit for selective attenuation of a

signal comprising:

a signal input port;

a non-linear circuit coupled to said input port and comprising:

a modified π attenuator network;

a pair of diodes coupled together in parallel and coupled to said

modified π attenuator network; and

a first resistor and a first inductor in series, said series coupling being

coupled in parallel to said coupled diodes; and

an output port for outputting said selectively attenuated signal from said non¬

linear circuit.

2. The distortion control circuit of claim 1 further including a low

resistance D.C. bias voltage circuit.

3. The distortion control circuit of claim 2 further including a temperature

compensation circuit coupled with said bias circuit, for selectively adjusting said

D.C. bias voltage in response to a change in ambient temperature.

4. The distortion control circuit of claim 1 wherein said first resistor

generates a voltage proportional to said input signal; whereby said proportional voltage creates a non-linear current through at least one of said diodes in said pair,

thereby creating a non-linear resistance to selectively attenuate said signal.

5. The distortion control circuit of claim 3 wherein said temperature

compensation circuit comprises:

a constant current source transistor;

a second transistor, coupled to the output of said current source transistor, for

outputting said D.C. bias voltage;

a linearized resistance circuit having a thermistor coupled in parallel to a

second resistor; and

a variable resistor that couples said current source transistor to said linearized

resistance circuit;

whereby the linearized resistance circuit is correlated to a change in ambient

temperature.

6. The distortion control circuit of claim 1 whereby said non-linear circuit

provides selective attenuation of the signal based upon the signal magnitude;

whereby less attenuation is provided for larger signal magnitudes and more

attenuation is provided for smaller signal magnitudes.